计算定积分：∫(0,π)x[(sinx)^m]dx=

Im=∫[0,π]x(sinx)^mdx=∫[0,π]x(sinx)^(m-1)d(-cosx)=-cosx*x(sinx)^(m-1)|[0,π]+∫[0,π]cosxdx(sinx)^(m-1)=∫[0,π]cosx*sinx^(m-1)dx+(m-1)∫[0,π]x(cosx)^2(sinx)^(m-2)dx=∫[0,π]sinx^(m-1)dsinx +(m-1)...